# Question: A freshly brewed shot of espresso has three distinct components

A freshly brewed shot of espresso has three distinct components: the heart, body, and crema. The separation of these three components typically lasts only 10 to 20 seconds. To use the espresso shot in making a latte, a cappuccino, or another drink, the shot must be poured into the beverage during the separation of the heart, body, and crema. If the shot is used after the separation occurs, the drink becomes excessively bitter and acidic, ruining the final drink. Thus, a longer separation time allows the drink maker more time to pour the shot and ensure that the beverage will meet expectations. An employee at a coffee shop hypothesized that the harder the espresso grounds were tamped down into the portafilter before brewing, the longer the separation time would be. An experiment using 24 observations was conducted to test this relationship. The independent variable Tamp measures the distance, in inches, between the espresso grounds and the top of the portafilter (i. e., the harder the tamp, the greater the distance). The dependent variable Time is the number of seconds the heart, body, and crema are separated (i. e., the amount of time after the shot is poured before it must be used for the customer’s beverage). The data are stored in Espresso.

a. Use the least squares method to develop a simple regression equation with Time as the dependent variable and Tamp as the independent variable.

b. Predict the separation time for a tamp distance of 0.50 inch.

c. Plot the residuals versus the time order of experimentation. Are there any noticeable patterns?

d. Compute the Durbin Watson statistic. At the 0.05 level of significance, is there evidence of positive autocorrelation among the residuals?

e. Based on the results of (c) and (d), is there reason to question the validity of the model?

f. What conclusions can you reach concerning the effect of tamping on the time of separation?

a. Use the least squares method to develop a simple regression equation with Time as the dependent variable and Tamp as the independent variable.

b. Predict the separation time for a tamp distance of 0.50 inch.

c. Plot the residuals versus the time order of experimentation. Are there any noticeable patterns?

d. Compute the Durbin Watson statistic. At the 0.05 level of significance, is there evidence of positive autocorrelation among the residuals?

e. Based on the results of (c) and (d), is there reason to question the validity of the model?

f. What conclusions can you reach concerning the effect of tamping on the time of separation?

**View Solution:**## Answer to relevant Questions

The owners of a chain of ice cream stores have the business objective of improving the forecast of daily sales so that staffing shortages can be minimized during the summer season. As a starting point, the owners decide to ...In Problem 12.4 on page 423, you used the percentage of alcohol to predict wine quality. The data are stored in VinhoVerde. From the results of that problem, b1 = 0.5624 and Sb1 = 0.1127. a. At the 0.05 level of ...The volatility of a stock is often measured by its beta value. You can estimate the beta value of a stock by developing a simple linear regression model, using the percentage weekly change in the stock as the dependent ...Based on a sample of n = 20, the least squares method was used to develop the following prediction line: ŷi = 5 + 3Xi. In addition, a. Construct a 95% confidence interval estimate of the population mean response for X = 4. ...What is the interpretation of the Y intercept and the slope in the simple linear regression equation?Post your question